multilayer immobilized-enzyme filter reactors: urease bound to nylon fabric filters

Multilayer Immobilized-Enzyme Filter Reactors: Urease Bound to Nylon Fabric Filters

LEV SHEMER, School of Engineering, and RON1 GRANOT, AMIHAY FREEMAN, MORDECHAI SOKOLOVSKY, and

LEON GOLDSTEIN,?' Dc>partment of Biochemistry, The George S . Wise Center of Lif> Sciencc.s, Tcl-A\tiv University, Tel-Aviv,

Isra c 1

Summary Urease was bound to commercially available nonwoven nylon fabric filters. Mul-

tilayer immobilized-enzyme filter reactors were constructed by packing varying numbers of urease-nylon filters in a column. Owing to the relatively open structure and high mechanical strength of the filter fabric, compaction and pressure drop effects were minimal. The reactors could be operated in a wide range of substrate concentrations and flow rates under conditions where mass-transfer limitations could be neglected. The kinetic behavior of the immobilized-enzyme filter reactors could be described by a linear form of the integrated Michaelis-Menten equation using a model based on the sequential action of the enzyme filters.

INTRODUCTION

The numerous techniques for covalent fixation of enzymes onto solid supports developed in the last decade' made possible the design of enzymatic continuous-flow reactors of a variety of con- figurations. 2*3 Continuous packed-bed or stirred-tank reactors con- taining enzymes attached to particulate supports are used in several industrial p r o c e ~ s e s . ~ * ~ Packed-bed and tubular reactors or varia- tions thereof are also used as components of various analytical and monitoring devices as well as extracorporeal circulation systems for the treatment of certain metabolic disorders caused by enzyme defi~iencies.~,~*' The kinetics of such systems is often dominated by internal diffusion and mass-transfer effects. 2,8-14

This paper describes the kinetic behavior of multilayer irnmobi-

* To whom correspondence should be addressed.

Biotechnology and Bioengineering, Vol. XXI, Pp. 1607-1627 (1979) @ 1979 John Wiley & Sons, Inc. 0006-3592/79/0021-1607$01 .OO

1608 SHEMER ET AL.

lized-enzyme filter reactors based on urease bound covalently to commercially available nylon filters (see also Ref. 15).

The filter material (spun-bonded nylon) is a nonwoven polyamide fabric manufactured by spinning continuous filaments of nylon 6,6 in a random web formation and bonding the filaments at the cross- over points without adhesives or other additives (Fig. I ) . Nonwoven nylon fabrics have high mechanical strength and dimensional sta- bility, and because of their relatively open structure-low hydro- dynamic resistance. Stacks of such filters exhibited no significant compaction or pressure drop effects.

Aminoaryl functional groups were introduced on the filter fabric by procedures described in earlier communications from our labo- ratory, 16-19 and urease bound to the modified filter fabric by the azo method. Multilayer filter reactors constructed by packing varying numbers of urease-nylon filters in a column could be operated in a wide range of substrate concentrations and flow rates under conditions where the kinetics of the reaction dominate the catalytic process.

The behavior of the reactors in the diffusion-free regime could be described by a model based on the sequential action of the enzyme filters.

Fig. I . Nonwoven nylon fabric (Cerex@, type I I , Monsanto Co.) as seen under the microscope. Magnification x 66.

MULTILAYER IMMOBILIZED-ENZYME FILTER REACTORS 1609

MATERIALS AND METHODS

Spun-bonded nylon fabric (CerexQ, type 1 I ; 5 denier; nylon 6,6) was obtained from Monsanto Co. (St. Louis, MO). The specifica- tions are: mean thickness of fabric, 0.2 mm; fabric weight, 6.9 mg/ cm2 (2 oz./yd.2); specific gravity of nylon 6,6, 1.14 g/cm3. Disks of 30 mm diam were cut from the nylon fabric.

Urease (type 111, a partially purified preparation) was supplied by Sigma Chemical Co. (St. Louis, MO). Urea, analytically pure, was obtained from E. Merck (Darmstadt, W. Germany). All other re- agents and buffer salts were of the purest grade available commercially.

Atninoaryl Polyac~rvlamidr-Nvlon Deri,wtiw

Aminoaryl functional groups were introduced on the surface of the nylon filaments of the nonwoven filter fabric disks by grafting linear polyacrylamide (molecular weight of 170000) partially substituted with 4-amido-4’-aminodiphenylmethane groups (see Fig. 2) as described by Freeman et al.l6-I8

CONH2 f

Fig. 2 . Chemical structure of modified nylon filament.

1610 SHEMER ET AL.

Coupling of Urease t o Aininoaryl Polyac.rylainide-Nvloii Disks

A glass column packed with 100 aminoaryl polyacrylamide-nylon disks of 30 mm diam was activated by circulating cold 1% sodium nitrite in O.1M HCl (100 ml) at a rate of 2-3 ml/min. The activated column was washed with cold water (100 ml). A solution of urease (5 mg/ml; 40 ml) in O.1M phosphate buffer (pH 8) was circulated through the column at 4°C for 18 hr. The urease-nylon disks were washed (by circulation) with cold water (500 ml), IM KCl (200 ml), and water (100 ml) and stored under water at 4°C.

Bound protein was estimated by amino acid analysis of acid hydrolysates of urease-nylon conjugates as previously described. l63I7

APPARATUS

The enzyme reactor consisted of a Perspex column (height 70 mm, 30 mm i.d.) fitted with a perforated hollowed-out base and a screw top. The inlet and outlet tubes (1.8 mm i.d.) were made of stainless steel and connected with the feed and affluent reservoirs by Tygon tubing. The reactor was loaded with varying numbers of urease-nylon filter disks of 30 mm diam. Constant packing of the disks was maintained by means of Perspex fillers of varying heights having a 5 mm diam central channel and a conical hollowed-out base fitted with a rubber O-ring. Additional support for the enzyme- nylon disks was obtained by putting a sintered glass filter on top of the filter stack.

The feed flow rates, measured by collection, were controlled by varying the height of the substrate solution reservoir, thus varying the hydrostatic pressure head. For low flow rates a peristaltic pump (Buchler) was used. All substrate solutions were thermostated at 25°C.

ASSAY METHODS

The enzymatic activity of urease was measured by the nitroprus- side method for the colorimetric determination of ammonia (at 625 nm) according to Chaney and Marbach.20,21 The activity was calculated from the intercept of the appropriate Eadie-Hofstee plot and expressed as the amount of substrate transformed per unit time (pmol urea decomposed/min) at 25°C per mg protein.

The activity of the urease-nylon filters was obtained from the


measured feed rate ( Q ) and the ammonia concentration in the effluent from a reactor loaded with a small number of disks ( N = 1-10), operated at high flow rates, Q > 40 mVmin (where the chemical reaction is kinetically controlled) and under conditions where the degree of conversion (Y) is low. The activity per disk (pmol urea decomposed/min/disk) was calculated from the intercept of the appropriate Eadie-Hofstee plot of eq. (12) in the form YJoQ/ N = Vmaxul/(l + K,' /So) (for details see Results and Discussion section and legend to Table I).

All solutions used in the enzyme assays were made up in O.1M phosphate buffer (pH 7.0), 10-3M in EDTA. The kinetic experiments were carried out at 25 ? 0.1 "C.

THEORETICAL CONSIDERATIONS

The multilayer immobilized-enzyme filter reactor to be dealt with is composed of a number of thin, permeable nylon fabric disks. The nonwoven nylon fabric consists of several layers of randomly oriented filaments, uniformly coated with enzyme (Fig. 1 ) .

A simple mathematical model can be based on the following considerations:

i) The catalytic capacity of a single-enzyme filter disk is relatively small. Within a wide range of flow rates and substrate concentrations, the degree of conversion of substrate per disk (Xi) would hence be very low, i.e., X i << 1 .

i i ) By a similar reasoning, the substrate concentration gradient generated by the chemical reactor within a single-enzyme filter disk will be relatively small.

i i i ) It is also assumed that a uniform and essentially flat substrate concentration profile will be established before the substrate solution reaches the next filter. The plug form of the concentration profile can be ascribed to convective effects in the plane perpen- dicular to the direction of flow, arising from the random web structure of the filter filaments.

iv) On the basis of these assumptions, a flow reactor consisting of N filter disks could, in principle, be characterized in terms of the kinetic and flow parameters determined for a single-enzyme filter. The overall kinetic behavior of an N-disk reactor could then be described by the sequential action of N single-enzyme filters arrayed in series, where the output concentration of substrate and product

TA

BL

E I

Bin

ding

of

Ure

ase

to N

ylon

Fab

ric

Filte

rss

Prot

ein

cont

entb

En

zym

e ac

tivity

d 0%

) (p

mol

ure

a hy

drol

yzed

lmin

)

per g

filte

r pe

r cm

* filt

er

per g

filt

er

per

cm2 f

ilter

Pe

rcen

t act

ive

Prep

arat

ion

fabr

ic

fabr

ic

per

filte

r dis

k'

fabr

ic

fabr

ic

per f

ilter

dis

kc

prot

ein

A

10

0.06

9 0.

49

I 85

I .28

9.

I 76

B

I1

0.07

6 0.

54

213

I .48

10

.5

79

Cer

exe,

type

I I,

Mon

sant

o C

o.:

nylo

n 6,

6 no

nwov

en (

spun

bon

ded)

fabr

ic, 5

den

ier (

for a

dditi

onal

spe

cifi

catio

ns se

e te

xt).

All

num

bers

Det

erm

ined

by

amin

o ac

id a

naly

sis

of a

cid

hydr

olys

ates

of

urea

se-n

ylon

fi

lters

. Fi

lter d

isk

diam

eter

is 3

0 m

m.

Spec

ific

act

ivity

of

nativ

e ur

ease

(Si

gma,

type

111

): 24

.5 p

mol

ure

a hy

drol

yzed

/min

/mg

prot

ein.

give

n in

tabl

e ar

e m

ean

valu

es o

f m

easu

rem

ents

on

thre

e di

sks

rem

oved

at r

ando

m f

rom

a s

tack

of

100-

200

urea

se-n

ylon

filt

er d

isks

.

'' Cal

cula

ted

from

the

inte

rcep

t of

Eadi

e-H

ofst

ee p

lot

eq. (

12).

YJ,

,Q/N

=

Vm

axu,

/(1 +

K,,,

'/SJ

as d

escr

ibed

in te

xt.

cn E 3 rn P


of the ith disk serves as the input concentration for the (i + 1)th disk.

v) Since the enzyme on the surface of the nylon filaments consists of a very thin layer, internal diffusion resistances are assumed to be negligible. Moreover, at sufficiently high flow rates mass-transfer effects would also be negligible.8,9,14 The kinetically controlled enzymatic reaction would then obey the Michaelis-Menten scheme.

In the absence of substrate and product inhibition effects, the degree of conversion of substrate by a single-enzyme filter, X i , can be described by the integrated Michaelis- Menten equation written in the form:22

Si-lXi - Km' ln(1 - X i ) = Vmaxy/Q (1)

Where is the input concentration of substrate for the ith filter disk, Q is the volume flow rate, and K m ' , V,,,, and v, are the Michaelis constant, maximal reaction velocity (in units of concentration of substrate transformed per unit time), and void volume, respectively, for a single-enzyme filter.

The logarithmic term of eq. ( 1 ) can be approximated by its series ex pan sion

(2 1 Retaining the first term of eq. (2) for very low values of Xi

(X i << I ) , a simple explicit solution of eq. ( 1 ) can be obtained for the degree of conversion, X i , at the ith filter disk

ln(1 - X i ) = - X i - ( X i 2 / 2 ) . . -

4 = Vmax ~/Q(si-l + K m ' )

xi = (Si-1 - & ) / & - I

(3 1

(4)

(5 )

Where

If Yi is the overall degree of conversion for i disks,

yi = (So - &)/So

(obviously Yo = 0) it can be easily shown from eqs. (3)-(5) that

where the parameters p and 5, nondimensional Michaelis constant and maximal conversion capacity per single filter, are given by

P = K m ' / S o (7)

4 = Vmax s / S O Q (8)

1614 SHEMER ET AL.

The degree of conversion for a given number of filter disks can thus be calculated by sequential solution of eq. (6) using the appropriate values for p and ,$ as illustrated in Figure 3 for ,$ = 0.01 and 0.10 and p = 0.10 and 1.00.

In the limiting case of low overall degree of conversion, Y << I , eq. (6) reduces to

&+I = yi + , $ / ( I + P ) = (i + 1 > [ , $ / ( 1 + PI1 (9)

(94 i.e.,

yN = ",$ / ( l + p)1 The degree of conversion of substrate in a multilayer enzyme

filter reactor would vary linearly with the number of filters ( N ) as long as Y << I obtains (see Fig. 3).

If in addition the initial substrate concentration, So, is high relative to Km', i.e., p << 1 , the overall degree of conversion for N filters is given by

YN = N,$ (10)

It should be mentioned that the model, used to derive the expres- sions for the simple Michaelis-Menten case, can be easily extended to accommodate the various types of inhibition phenomena.29

RESULTS AND DISCUSSION

Preparation and Characterization of Urcasc~-NyIon Filters

The nonwoven polyamide fabric (mean fabric thickness 0.2 mm) consists of a web of several layers of randomly oriented nylon

<=oi .p=oi &=ai.p=io E * O O l , p=ot

N

Fig. 3. Theoretical Y vs. N curves for different values of p and .f. calculated by eq. (6) (-) and by eq. (9) (---).

MULTILAYER IMMOBILIZED-ENZY ME FILTER REACTORS 1615

filaments. The mean diameter of the fabric filaments determined under the microscope was 25 2 2 nm (Fig. I ) . Disks of 30 mm diam were cut from the nylon fabric. The void volume of the nylon filter disks, measured by passing a solution of blue dextran through a reactor packed with 200 filters, was 0.1 cm3/30 mm diam disk, in agreement with the value estimated using the specification supplied by the manufacturers: specific gravity of nylon 6,6 = 1.14 g/cm3; mean fabric weight = 6.9 mg/cmz for the 5 denier fabric, corresponding to about 12.5 m nylon filament yarn/cm2 fabric. From this data a void fraction E = 0.7 and overall filament area of 9.82 cmz/ cm2 fabric were calculated.

Aminoaryl functional groups were introduced on the surface of the constituent nylon filaments of the filter fabric by grafting linear polyacrylamide (molecular weight of 170000), partially substituted with 4-amido-4'-aminodiphenylmethane functional groups (-5 mol %) as described by Freeman et a1.l6-l8 The chemical structure of aminoaryl polyacrylamide-nylon is shown schematically in Figure 2.

The aminoaryl-nylon filter disks were activated to the corresponding diazonium salt and coupled with urease (for details of the procedures and chemical principles involved see Refs. 16- 19). The chemical modification of the filter fabric as well as the coupling of enzyme were affected by the sequential circulation of the appropriate reagent solutions through a stack of spun-bonded nylon disks loaded in a glass column. This procedure ensured that the protein content and enzymatic activity of individual urease-nylon disks in a batch would be essentially uniform.

Two batches of urease-nylon filters were prepared. Table I summarizes data on the mean protein contents and enzymatic activities of the two preparations (A and B) determined in each case on three filter disks removed at random from the urease-nylon filter stack (the variation between individual disks was no more than 5%). The high specific activity of the immobilized protein (about 80% of that of native urease) strongly suggests that under the conditions of the rate assay no significant diffusional limitations are present (for a more detailed discussion see Kinetics section).

The urease-nylon filters were used intermittently for six months without a detectable loss of activity.

Kin P tic Be I1 a r i o r oj' Mii It ilavc r UrcJa s c - Nvlo n Filt P r Re a c' t o rs

Table I 1 summarizes results of continuous urea hydrolysis experiments carried out in a column reactor loaded with 2 to 208 urease- nylon filter disks of 30 mm diam at substrate concentrations 5 to

TA

BL

E I

1 D

egre

e of

Con

vers

ion

of U

rea,

Y, a

t the

Exi

t of

Mul

tilay

er U

reas

e-N

ylon

Filt

er R

eact

orsa

Flow

rat

e, Q (m

umin

) U

rea

A

N (m

M)

12

21

46

62

25

10

50

100

250

10

5 10

50

I00

250

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0.

04

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0.

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74)

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15)

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9 0.

032

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6 0.

0 I3

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3 0.

013

0.00

6 0.

0044

(0

.023

) [0

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8]

(0.0

13)

(0.0

06)

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045 )

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v1

X

(0.0

13)

[O.O

I071

(0

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(0.0

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(0

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m

0.00

54

0.00

33

0.00

15

0.00

118

(0.0

057)

[0

.004

6]

(0.0

033)

(0

.00l

5)

(0.0

011)

m rn

6.0

12.0

40

60

> r

(0.0

60)

[0.0

484]

(0

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) (0

.016

) (0

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4

0.42

0.

24

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(0.5

7)

[0.3

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(0.3

29)

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(0.1

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(0.0

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65

5 10

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(0.5

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(M

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[0.6

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[0.2

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[0

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[0

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3.0

6.0

7.0

15

24

a N

= n

umbe

r of

urea

se-n

ylon

filt

er d

isks

. Val

ues

in p

aren

thes

es w

ere

calc

ulat

ed u

sing

eq.

(6) w

ith K

,’ =

15.

2mM

and

V,,,

=

9lm

M//m

in/

disk

for

N =

2,

10, a

nd 1

4 (p

art A

) an

d V

,,,

=

105m

M/m

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1620 SHEMER ET AL.

250m.M and flow rates 2.5 to 62 ml/min. Under these conditions the Reynolds numbers based on the reactor diameter did not exceed 100. The data are presented as the degree of conversion of urea at the exit of the reactor.

To compare the observed kinetic behavior of the multilayer urease-nylon filter reactors with that predicted by eq. (6), Km’ and V,,,, from which the dimensionless quantities p and ,$ can be evaluated, must be known. It should be remembered that eq. (6) and its simplified forms [eqs. (9) and (lo)] were derived on the basis of the assumption that internal diffusion resistances were unimportant and mass-transfer effects negligible at sufficiently high flow rates, i.e., that the enzymatic reaction is kinetically controlled and follows the Michaelis-Menten scheme (see also Refs. 2, 8, 9, 13, 14).

The kinetic parameters V,,, and K,’ for a single urease-nylon filter disk could be extracted from the experimental results in the regions where eqs. (9) and (10) are obeyed, i.e., in the regime of kinetic control, at very low degrees of conversion ( Y , << 1 ) where Y N varies linearly with N.

By eq. (9), the conversion of substrate per disk, Xi, is given by

Xi = YN/N = ,$/(l + p )

(1 1) - Vmax 01 -

QSo(1 + Km’/So) The dependence of the reaction rate per disk, u (expressed in

units of concentration of substrate transformed per unit time) on the initial substrate concentration, So, can be described by the equation

identical in form to the Michaelis-Menten relation ( v l in eq. (12) is in effect a proportionality factor whereby enzymatic activities, YJoQIN, in units of amount per unit time are converted into reaction rates, in units of concentration per unit time).

I t follows from eq. (12) that the experimentally determined reaction rate per disk, v (= Y,J,,QINvJ, should be independent of the flow rate at all values of Q , provided mass-transfer limitations are absent, and would depend only on the initial substrate concentration, S o . Moreover, under the conditions where eq. (12) obtains, if K ,,,I is known, the reaction rate, I!, when multiplied by ( I + Km’/So)


should be constant, Vmax, at all substrate concentrations and flow rates.

The kinetic data of Table IIA, for 2, 10, and 14 urease-nylon filters, recalculated per filter disk according to eq. (12) and plotted as v vs. Q and as v ( l + K,’ /So) vs. Q are shown in Figure 4.

Above a bulk flow rate Q = 20 ml/min (corresponding to a linear velocity u = 0.07 cdsec) , limiting values of v , independent of flow rate, and hence free of mass-transfer limitations, are obtained at all substrate concentrations (Fig. 4(a)). The limiting reaction rates obtained at each value of So can be used to calculate the intrinsic values of V,,, and K,’ by one of the conventional graphic proce-

1 L-.L---, I 10 20 30 40 50 60 70 80 (a)

FLOW RATE (ml/min)

Fig. 4. Dependence of the rate of urea hydrolysis catalyzed by a single urease- nylon filter on the feed flow rate. (a) Rate of a single urease-nylon filter, 1 3 = Y J , /Nu,, as a function of feed flow rate, Q (see eq. (12)). (b) I , ( I + K,’ /S , ) as a function of feed flow rate (Insert: mean effectiveness factor, 7 . estimated from u( I + K,’/So) vs. Q plot.) Open symbols: two enzyme filters, half-filled symbols: 10 enzyme filters: filled symbols: 14 enzyme filters. (0. 8. 0) 5mM urea: (v. A. v) lOmM urea: (A. A A) 50 mM urea: (0, m. B) IOOmM urea: (0 @a 250 mM urea.

1622 SHEMER ET AL.

dures based on the linearized forms of the Michaelis-Menten relation, eq. (12).

The 1 3 vs. S and 1’ vs. v/S plots of the data for 2, 10, and 14 urease-nylon filters (Fig. 4(a) and Table IIA) are shown in Figure 5 . From the Eadie-Hofstee plot (insert Fig. 5) V,,, = 9lmM/min/ disk and K , ’ = 15.2mM were calculated by least-squares fit. In another set of experiments with a different batch of urease-nylon disks (Table IIB), V,,, = 105mM/min/disk and the same value of K , ‘ (15.2mM), essentially identical to that obtained for native urease ( K , = 16mM) were calculated by the same procedure.

The close similarity in the values obtained for the apparent Mi- chaelis constant of soluble and filament bound urease (in the latter case at flow rates where mass-transfer is eliminated) lends support to the assumptiom underlying the model employed, i.e., that internal diffusional resistances are unimportant, the enzyme being located at or near the catalyst surface. Additional support for this view is obtained from the high specific activity of the bound protein (80% of that of the native enzyme; Table I) and by replotting the data of Figures 4 and 5 in the form of a normalized Eadie-Hofstee plot as suggested by Horvath and E n g a ~ s e r . ~ ~ , ~ ~ As can be seen in Figure 6, the experimental points fall on the theoretical straight line calculated for a kinetically controlled reaction.

100 l------

Fig. 5 . Michaelis-Menten and Eadie-Hofstee plots for a single urease-nylon filter. Symbols the same as in Figure 4. (-) Calculated using K ,,,‘ = 15.2mM and V,,, = 9lmW/rnin/disk (see eq. (12)).


Fig. 6. Normalized Eadie-Hofstee plot for a single urease-nylon filter. Data of Figure 5. (0) Two enzyme filters: (0) 10 enzyme filters: (0) 14 enzyme filters.

It should be mentioned that in contrast to several reports in the literature, indicating that urease is inhibited at high concentrations of s u b ~ t r a t e ~ ~ - ~ ~ and noncompetitively by p r o d u ~ t , ~ ~ , ~ ~ no detectable inhibition effects by either urea (5 to 250mM) or by ammonium ion were found with urease-nylon filter reactors, under the conditions employed.

Following the determination of the diffusion-free values of the Michaelis- Menten parameters, an additional test, based on replotting the data of Figure 4(a) according to eq. (12), as I,( 1 + K m’/So) vs. Q , could be applied to delineate the region where the kinetic behavior of urease-nylon filter reactors is no longer independent of mass-transfer limitations (Fig. 4(b)): above Q = 20 ml/min, corresponding to Reynolds numbers (based on filament diameter, d = 25 pm) larger than 0.02, the values of I!( I + Km’/So) are independent of Q . all points falling on the same straight line (V,,, = 91 * 5mM/ min/disk) parallel to the Q axis. Below this value of Q . i t ( I + K m‘/ So) decreases progressively as Q decreases: viz. as the Reynolds and correspondingly the Sherwood number decrease, mass-transfer effects become more pronounced and eq. (12) is not obeyed (see Fig. 4(b)).

From the data of Figure 4(b) a mean effectiveness factor, 7, defined as the ratio of the actual reaction rate to the rate in the absence of mass-transfer limitations could be estimated (see insert to Fig. 4(b)). The value of 7 at each flow rate was averaged over

1624 SHEMER ET AL.

all initial substrate concentrations since the available data did not allow a more accurate analysis. Because no experiments were carried out with a small number of filter disks (2- 14) at very low flow rates (Q < 6 ml/min; see Table IIA), in this range 7) was estimated by extrapolation (dashed line in insert to Fig. 4(b)).

Using the values of K,’ and V,,, obtained from the data of Figure 5 , the dimensionless parameters p and 5 could be evaluated by eqs. (7) and (8).

The numbers in parentheses in Table 11 give the theoretical degrees of conversion using a value of K,’ = 15.2mM and V,,, = 9lmM/min/disk for 2, 10, and 14 disks (Table IIA) and V,,, = 105mM/min/disk for 65, 93, and 208 disks (Table IIB). Reasonably good agreement between calculated and experimental values is obtained in the diffusion free region (Q > 20 ml/min) in the whole range of N and So investigated.

At low flow rates the theoretical degrees of conversion calculated according to eq. (6) are higher than those observed experimentally. In most cases the discrepancy between Ythr,,r and YcsXpt could be reduced considerably by multiplying the dimensionless maximal conversion capacity per disk, 6, in eq. (6), by the mean effectiveness factor deduced for the appropriate flow rate, from the data of Figure 4(b) (Table 11; values in square brackets).

CONCLUDING REMARKS

A simple model could provide a description of the kinetic behavior of multilayer immobilized-enzyme filter reactors, a special case of plug-flow reactors, by reason of several features characteristic of the reactor configuration.

i ) The reaction rate of enzymes immobilized on the surface of the filter-fabric nylon filaments is not significantly affected by internal diffusional restrictions.

i i ) Mass-transfer effects in a stack of enzyme filters can be eliminated at relatively low linear velocities by virtue of the random web orientation of the filter-fabric filaments and the low catalytic activity of a single-enzyme filter.

i i i ) An elementary structural component of the reactor, a single- enzyme filter disk, can be isolated and characterized separately under conditions where the limitations arising from both internal diffusion and mass transfer have been effectively eliminated.

The kinetic behavior of a reactor consisting of any number of enzyme filters could hence be predicted over a wide range of flow


rates, in terms of the kinetic parameters obtained for a single-enzyme filter, in the diffusion-free regime, using a linearized form of the integrated Michaelis- Menten equation.

Furthermore, since mass-transfer effects depend on the linear velocity ( u ) and the Reynolds number based on the microscopic geometric parameters of the system (the diameter of the constituent filaments of the filter fabric in our case), the same critical values of 11 and Re, delineating the region where kinetic control predominates, would presumably obtain irrespective of the size (i.e., macroscopic diameter) of the enzyme 'filter disks.

In addition, owing to the random web orientation of the filaments and the relatively open structure of the filter fabric, the external diffusion-free regime is attained in the case of multilayer immobilized-enzyme filter reactors at considerably lower values of u and Re as compared to tubular or conventional packed-bed reactors. (Compare for example if = 0.07 cm/sec in our case with u = I cm/ sec in a plug-flow reactor of 2.5 cm diam packed with glucose oxidase immobilized on nonporous glass beads of 40-60 mesh13 and 11 = 50 cm/sec for a chymotrypsin-coated tubular reactor of 0.125 in. i.d.14)

In conclusion, the behavior of the multilayer immobilized-enzyme filter reactors in the regime of kinetic control, which was mainly emphasized in this paper, is relatively well understood. More in- formation on the behavior of these reactors in the region of low flow rates where mass-transfer effects cannot be ignored has yet to be provided.

Nomenclature diameter apparent Michaelis constant for native enzyme apparent Michaelis constant for immobilized enzyme number of enzyme filter disks in reactor feed flow rate (ml/min) Reynolds number (= ud/u) initial substrate concentration (M) input substrate concentration of ith enzyme-filter disk (M) linear feed flow rate (cdsec) void volume of single-enzyme filter disk (ems) total volume of single-enzyme filter disk (ems) reaction rate (Mlmin) maximal reaction rate (Mlmin) degree of conversion for a single (ith)-enzyme filter disk overall degree of conversion of reactor overall degree of conversion for reactor consisting of N-enzyme filter

disks

1626 SHEMER ET AL.

E void fraction (= v l /u t ) 7) effectiveness factor U kinematic viscosity (cm*/sec) P 6

dimensionless Michaelis constant (= K,’ /S , ) dimensionless maximal conversion capacity of single-enzyme filter

disk ( = V,,, u,/QSo)

This work was supported in part by National Council for Research and Develop- ment Grant No. 1856.

References 1 . L. Goldstein and G. Manecke, in Applied Biochemistry and Bioengineering

Vol. I . Immobilized Enzymes, Principles, L. B. Wingard, E . Katchalski-Katzir, and L. Goldstein, Eds. (Academic, New York, 1976), pp. 23-126.

2. W. R. Vieth, K. Venkatasubramanian, A. Constantinides, and B. Davidson, in Applied Biochemistry and Bioengineering Vol. 1. Immobilized Enzymes, Princi- ples, L. Wingard, E. Katchalski-Katzir, and L. Goldstein, Eds. (Academic, New York, 1976), pp. 221-327.

3. H. H. Weetall, Ed., Immobilized Enzymes, Antigens, Antibodies and Peptides (Marcel Dekker, New York, 1975).

4. E. K. Pyeand L. B. Wingard, Eds., Enzyme Engineering (Plenum, New York, 1974), Vol. 2.

5. H. H. Weetall and S. Suzuki, Eds.,Immobilized Enzyme Technology (Plenum, New York, 1975).

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7. T. M. S. Chang, Ed., Biomedicul Applicutions of Imrnobilizetl Eii:ymes and Proteins (Plenum, New York, 1977), Vols. I and 11.

8. C. Horvath and B. A. Solomon, Biotechnol. Bioeng., 14, 885 (1972). 9. B . J . Rovito and J. R. Kittrell, Biotechnol. Bioeng., 15, 143 (1973).

10. T. Kobayashi and K. J. Laidler, Biotechnol. Bioeng., 16, 99 (1974). 1 1 . T. T. Ngo and K. J. Laidler, Biochim. Biophys. Acta, 377, 317 (1975). 12. C. N. Satterfield, Mass Transfer in Heterogeneous Catalysis (MIT, Cam-

13. K . B. Ramachandran and D. D. Perlmutter, Biotechnol. Bioeng., 18, 669

14. S. Venkat Raman, T. A. Horbett, and A. S. Hoffman, J . Molec. Catal., 2,

15. A. K. Sharp, G. Kay, and M. D. Lilly, Biotechnol. Bioeng., 11, 363 (1969). 16. L. Goldstein, A. Freeman, and M. Sokolovsky, Biochem. J., 143,497 (1974). 17. A. Freeman, M. Sokolovsky, and L. Goldstein, J. Solid-Phase Biochem., 1,

261 (1976). 18. A. Freeman, R. Granot, M. Sokolovsky, and L. Goldstein, J . Solid-Phase

Biochem., 1, 275 (1976). 19. D. Blassberger, A. Freeman, and L. Goldstein, Biotechnol. Bioeng., 20, 309

(1978). 20. A. L. Chaney and E. P. Marbach, Clin. Chcm., 8, 130 (1962). 21. M. W. Weatherborn, Anal. Chem., 39, 971 (1961). 22. M. D. Lilly, W. E. Hornby, and E. M. Crook, Biochem. J., 100,718 (1966).

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23. C. Horvath and J . M. Engasser, Biotechnol. Bioeng., 16, 909 (1974). 24. J . M. Engasser and C. Horvath, in Applied Biochemistry and Bioengineering

Vol. 1 . Immobilized Enzymes, Principles, L. B. Wingard, E. Katchalski-Katzir, and L. Goldstein, Eds. (Academic, New York, 1976), pp. 127-220.

25. K . J . Laidler and J . P. Hoare, J. Am. Chem. Soc.. 71, 2699 (1949). 26. M. C. Wall and K . J . Laidler, Arch. Biochem. Biophys., 43, 299 (1953). 27. K . B. Ramachandran and D. D. Perlmutter, Biorechnol. Bioeng., 18, 685

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( 1976).

Accepted for Publication November 15, 1978

multilayer immobilized-enzyme filter reactors: urease bound to nylon fabric filters

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